The OP did specify what he wanted - the basic undergraduate and starting graduate curriculum. That's a pretty well defined area: Algebra, Real Analysis, Geometry and Topology with maybe some complex analysis, number theory, statistics, CS or etc thrown in.
I personally did work myself up to the graduate in math during the last two years of High School & first year of college. I was motivated by exploring ideas and gaining knowledge. I would guess that each person has a somewhat unique motivation strategy. Maybe solving problems gets some people doing stuff. I'm sure simply learning stuff can motivate others. Probably each person has to experiment to discover what works for them - I would pick up a calculus book and read it - well, I'd skim repeatedly and then read in depth, solving a few problems. Math is difficult, of course, so having a bit of patience with your until it gets the ideas on it's own is probably necessary.
> I personally did work myself up to the graduate in math during the last two years of High School & first year of college.
...how in the world did you manage to do this? Did you actually self-study, or were you placed in a gifted program? Self-studying all of undergraduate mathematics is more impressive than actually studying all of it in a four year classroom setting. Doing so as a teenager is amazing.
The most gifted person I've ever known in mathematics is actually a physicist who entered Harvard at 16. He was already taking undergraduate math courses at 13/14 and had mastered all the undergraduate material by the first semester of his undergraduate degree. For the remaining years of his undergraduate degree he took graduate math courses.
But in order to do that he needed to not only be gifted; he was placed in a program for extremely gifted kids sponsored by Stanford University from his preteen years. I don't think your anecdote is a great comparison for the OP's expectations (or for calibrating advice they'd benefit from).
How in the world did you manage to do this? Did you actually self-study, or were you placed in a gifted program?
I read quite a bit on my own, I took some courses at UCLA through a high school scholars program (including the undergraduate honors seminar). The entirety of the undergraduate program might be a slight exaggeration but I was ready for graduate level courses when I got to Berkeley.
I think going through the material requires determination, not necessarily being extremely gifted. But then, it seems like people at someone's gone through a bunch material say by that fact they're gifted. Thus having done this, one is tautologically gifted.
I've never tested at the extremely gifted level but I'm doubtful of single-measures of intelligence regardless.
Edit:
I don't think your anecdote is a great comparison for the OP's expectations (or for calibrating advice they'd benefit from).
Neither of us know the OP. It's kind of up to them to calibrate what process works for them. Scanning a lot of math until I found good, clear explanations worked well for me.
>>> I would guess that each person has a somewhat unique motivation strategy.
Indeed, speaking only for myself, I don't think that I had the self discipline to carry through with such a plan as a teenager. I needed the classroom environment to learn math & physics, which became my college majors. At the same time, I was able to teach myself programming and electronics quite easily for some mysterious reason. And I ended up combining all of those things in grad school.
Also, I only had access to the books and resources of a typical suburb with a decidedly anti-intellectual culture. The officials at my high school refused to offer a calculus course because they said it would be "elitist."
I personally did work myself up to the graduate in math during the last two years of High School & first year of college. I was motivated by exploring ideas and gaining knowledge. I would guess that each person has a somewhat unique motivation strategy. Maybe solving problems gets some people doing stuff. I'm sure simply learning stuff can motivate others. Probably each person has to experiment to discover what works for them - I would pick up a calculus book and read it - well, I'd skim repeatedly and then read in depth, solving a few problems. Math is difficult, of course, so having a bit of patience with your until it gets the ideas on it's own is probably necessary.